Simplify the following expression: $ q = \dfrac{-4t - 3}{3} - \dfrac{-9}{5} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{-4t - 3}{3} \times \dfrac{5}{5} = \dfrac{-20t - 15}{15} $ Multiply the second expression by $\dfrac{3}{3}$ $ \dfrac{-9}{5} \times \dfrac{3}{3} = \dfrac{-27}{15} $ Therefore $ q = \dfrac{-20t - 15}{15} - \dfrac{-27}{15} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-20t - 15 + 27 }{15} $ Distribute the negative sign: $q = \dfrac{-20t - 15 + 27}{15}$ $q = \dfrac{-20t + 12}{15}$